Understanding Radical Equations and Their Graphs

This video tutorial covers graphing radical equations, starting with the parent function y = √x. It explains how to determine the domain and range, and explores the effects of reflections over the x and y axes. The tutorial also discusses vertical and horizontal shifts, using points for accurate graph sketches, and analyzing domain and range in transformed functions. Advanced transformations, including the impact of negative signs and complex shifts, are also covered.

What is the domain of the parent function y = √x?

• -Infinity to 0

• -Infinity to Infinity

• 0 to Infinity

• 0 to 1

How does the graph of y = -√x differ from y = √x?

• It shifts down

• It shifts up

• It reflects over the x-axis

• It reflects over the y-axis

In which quadrant does the graph of y = √x point when both x and y are positive?

• Quadrant 1

• Quadrant 4

• Quadrant 2

• Quadrant 3

What happens to the graph of y = √x if you add 2 to the function?

• It shifts 2 units down

• It shifts 2 units to the right

• It shifts 2 units to the left

• It shifts 2 units up

How does the graph of y = √(x - 2) differ from y = √x?

• It shifts 2 units down

• It shifts 2 units up

• It shifts 2 units to the left

• It shifts 2 units to the right

What is the effect of multiplying the square root function by 2?

• The graph is compressed vertically

• The graph is stretched vertically

• The graph is stretched horizontally

• The graph is compressed horizontally

Where does the graph of y = √(x - 1) + 2 start?

• (0, 0)

• (1, 2)

• (2, 1)

• (2, 3)

What is the domain of the function y = 3 - √(x - 4)?

• 0 to Infinity

• 4 to Infinity

• -Infinity to Infinity

• -Infinity to 4

In which quadrant does the graph of y = 3 - √(x - 4) primarily lie?

• Quadrant 1

• Quadrant 4

• Quadrant 2

• Quadrant 3

What is the range of the function y = 3 - √(x - 4)?

• Negative Infinity to 0

• 3 to Infinity

• 0 to 3

• Negative Infinity to 3